Holt CA Course 1

9-4 Finding Angle Measures

MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.Also covered: AF1.1, MG2.1

California Standards

Holt CA Course 1

9-4 Finding Angle Measures

Additional Example 1: Finding an Unknown Angle Measure

Find each unknown angle measure.

71° + m1 = 90°–71° –71°

m1 = 19°

Since the angles are complementary, the sum of the angle measures is 90°.

1

71°

A. The angles are complementary.

Subtract 71° from both sides.

Holt CA Course 1

9-4 Finding Angle Measures

125° + m2 = 180°–125° –125°

m2 = 55°

Subtract 125° from both sides.

2125°

B. The angles are supplementary.

Since the angles are supplementary, the sum of the angle measures is 180°.

Additional Example 1: Finding an Unknown Angle Measure

Find each unknown angle measure.

Holt CA Course 1

9-4 Finding Angle Measures

m3 = 82° Congruent angles have the same measure.

3 82°

C. The angles are vertical angles.

Additional Example 1: Finding an Unknown Angle Measure

Find each unknown angle measure.

Since the angles are vertical angles, the angles are congruent.

Holt CA Course 1

9-4 Finding Angle Measures

31° + m4 + 31° = 180°

–62° –62° 62° + m4 = 180°

The sum of the measures is 180°.

D. BEA CED; mAED = 180°

m4 = 118°

Subtract 62° from both sides.

431°E

CB

DA

Additional Example 1: Finding an Unknown Angle Measure

Find each unknown angle measure.

Since BEA and CED are congruent, mCED = 31°.

mBEA + mBEC + mCED = 180°.

Add.

Substitute.

Holt CA Course 1

9-4 Finding Angle Measures

Check It Out! Example 1

Find each unknown angle measure.

65° + md = 90°–65° –65°

md = 25°

Subtract 65° from both sides.

d

65°

A. The angles are complementary.

Since the angles are complementary, the sum of the angle measures is 90°.

Holt CA Course 1

9-4 Finding Angle Measures

Check It Out! Example 1

Find each unknown angle measure.

145° + ms = 180°–145° –145°

ms = 35°

Subtract 145° from both sides.

s145°

B. The angles are supplementary.

Since the angles are supplementary, the sum of the angle measures is 180°.

Holt CA Course 1

9-4 Finding Angle Measures

Check It Out! Example 1

Find each unknown angle measure.

mt = 32° Congruent angles have the same measure.

t

32°

C. The angles are vertical angles.

Since the angles are vertical angles, the angles are congruent.

Holt CA Course 1

9-4 Finding Angle Measures

25° + b + 25° = 180°

–50° –50°

50° + b = 180°

The sum of the measures is 180°.

D. WZV XZY; mVZY = 180°

b = 130°

Subtract 50° from both sides.

Check It Out! Example 1

Find each unknown angle measure.

Since WZV and XZY are congruent, mXZY = 25°.

mWZV + mWZX + mXZY = 180°

Add.

Substitute.

b25°Z

XW

YV

Holt CA Course 1

9-4 Finding Angle Measures

–27° –27°27° + c = 90° The sum of the measures is 90°.

c = 63°

Subtract 27° from both sides.

Additional Example 2: Application

Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work.

Step 1: The angles labeled c and 27° are complementary. To find c, use properties of complementary angles.

Holt CA Course 1

9-4 Finding Angle Measures

–151° –151°

151° + a = 180° The sum of the measures is 180°.

a = 29°

Subtract 151° from both sides.

Additional Example 2 Continued

Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work.

Step 2: The angles labeled a and 151° are supplementary. To find a, use properties of supplementary angles.

Holt CA Course 1

9-4 Finding Angle Measures

b = 27° Vertical angles are congruent.

Additional Example 2 Continued

Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work.

Step 3: The angles labeled b and 27° are vertical angles. To find b, use properties of vertical angles.

Holt CA Course 1

9-4 Finding Angle Measures

–22° –22°22° + z = 90° The sum of the measures is 90°.

z = 68°Subtract 22° from both sides.

Check It Out! Example 2

Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work.

x 165°22°

z

y

Step 1: The angles labeled z and 22° are complementary. To find z, use properties of complementary angles.

Holt CA Course 1

9-4 Finding Angle Measures

–165° –165°

165° + x = 180° The sum of the measures is 180°.

x = 15°

Subtract 165° from both sides.

Check It Out! Example 2 Continued

Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work.

Step 2: The angles labeled x and 165° are supplementary. To find x, use properties of supplementary angles.

x 165°22°

z

y

Holt CA Course 1

9-4 Finding Angle Measures

y = 22° Vertical angles are congruent.

Check It Out! Example 2 Continued

Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work.

Step 3: The angles labeled y and 22° are vertical angles. To find y, use properties of vertical angles.

x 165°22°

z

y